General solution for differential equation

[bhsmith]

Homework Statement

y'' + cy' + 6y = 0 (where c is a constant)

I need to find y(t) which i believe is the equation for a general solution.

Homework Equations

It would be r^2 + cr + 6y = 0 then I need to find the roots and create the general solution. My problem is I don't know what to do about the c, can i take the c to be =1 or do I just create a solution with a general c, and if so how would I do that?

The Attempt at a Solution

 

[rock.freak667]

You'd need to solve for r using the quadratic equation formula and depending on whether the part in the sqrt sign is = 0, > 0 or < 0, would define the general solution.

 

[vela]

You can't arbitrarily set c to 1. You need to solve the general case. Start by finding the roots to the characteristic equation.

 

[hunt_mat]

If you really want to get rid of c, then you might think about rescaling y and x but that is the complicated solution.